An angle of 1.8 radians at the center of the circle subtends an arc of length 23.4cm.

Find:
(a) The radius of the circle
(b) The area of the sector enclosed by the arc and the radii.

r = 23.4/1.8 = 13

a = 1/2 * 13^2 * 1.8

please show the working

Why did the circle go to the party? Because it wanted to be the life of the arc! Let's get down to business and solve this problem.

(a) To find the radius of the circle, we can use the formula: arc length = radius * angle (in radians).

Given that the angle is 1.8 radians and the arc length is 23.4 cm, we can set up the equation as follows:

23.4 cm = radius * 1.8 radians

Let's solve for the radius:

radius = 23.4 cm / 1.8 radians
radius ≈ 13 cm

So, the radius of the circle is approximately 13 cm.

(b) To find the area of the sector enclosed by the arc and the radii, we can use the formula: area of sector = (angle / 2π) * πr².

Given that the angle is 1.8 radians and the radius is 13 cm, we can calculate the area of the sector as follows:

area of sector = (1.8 radians / 2π) * π * (13 cm)²
≈ (0.9 / 2) * 3.14 * (169 cm²)
≈ 0.45 * 3.14 * 169 cm²
≈ 238.638 cm²

So, the area of the sector enclosed by the arc and the radii is approximately 238.638 cm².

Hope you found this circus act of solving the problem amusing!

To find the radius of the circle and the area of the sector, we can follow these steps:

(a) Finding the radius of the circle:
1. Recall that the angle at the center of a circle is equal to the ratio of the arc length it subtends to the radius of the circle.
So, we have the equation: angle = arc length / radius

2. Substitute the given values into the equation:
angle = 1.8 radians
arc length = 23.4 cm

3. Rearrange the equation to solve for the radius:
radius = arc length / angle

4. Calculate the radius:
radius = 23.4 cm / 1.8 radians

Therefore, the radius of the circle is approximately 13 cm.

(b) Finding the area of the sector:
1. Recall that the area of a sector is equal to the ratio of the angle at the center to the total angle of the circle, multiplied by the total area of the circle.
So, we have the equation: area of sector = (angle / 2π) * π * radius^2

2. Substitute the given values into the equation:
angle = 1.8 radians
radius = 13 cm

3. Calculate the area of the sector:
area of sector = (1.8 radians / 2π) * π * (13 cm)^2

Therefore, the area of the sector enclosed by the arc and the radii is approximately 134.64 cm^2.